Answer first
What this calculator tells you
Calculate the volume of a triangular prism from the triangle's base and height and the prism's length. Find how much a wedge, a roof space or a tent holds. Formula: Base area = ½ × base × height; volume = base area × length. At the worked-example inputs, the volume is 120. Holding every other input steady, moving triangle base from 4.8 to 7.2 moves the result from 96 to 144.
Transparent method
The formula
Find how much a wedge, a roof space or a tent holds.
Worked example
Example inputs
How to interpret the result
A prism's volume is the area of its end shape times its length, and here that end shape is a triangle. A triangle 6 wide and 4 high covers 12, so a prism 10 long holds 120 cubic units. Roof spaces, tents and wedge-shaped planters all work this way, and the only fiddly part is measuring the triangle's height at a right angle to its base.
At the worked-example inputs the volume is 120. It rises with triangle base, triangle height and prism length.
Formulas assume ideal geometric shapes. Real-world measurements carry their own error, and every input must use the same unit: mixing feet and inches silently produces a wrong answer.
Before you rely on it
What to check
Take the triangle's height straight up from the base to the peak. A sloped side is longer and gives a bigger area than the triangle really has.
The common error
Where people go wrong with triangular prism volume calculator
Forgetting the one half in the triangle's area. Without it you get the volume of a box, twice the size of the wedge.
Sensitivity evidence
How triangle base changes the volume
Holding every other input at the worked-example value, moving triangle base from 4.8 to 7.2 moves the volume from 96 to 144: a spread of 48, or 40% of the worked-example result.
| Triangle base | Volume | Triangle base area |
|---|---|---|
| 4.8 | 96 | 9.6 |
| 5.4 | 108 | 10.8 |
| 6worked example | 120 | 12 |
| 6.6 | 132 | 13.2 |
| 7.2 | 144 | 14.4 |
Every input, tested
Which input moves the volume most
Of the 3 inputs, triangle base moves the volume most (24 across the range tested) and prism length moves it least (24).
| Input | Tested from | To | Volume at each end | Swing |
|---|---|---|---|---|
| Triangle base | 5.4 | 6.6 | 108 to 132 | 24 (20%) |
| Triangle height | 3.6 | 4.4 | 108 to 132 | 24 (20%) |
| Prism length | 9 | 11 | 108 to 132 | 24 (20%) |
Two variables at once
Volume by triangle base and triangle height
Across the grid the volume runs from 76.8 to 172.8. Moving triangle base from 4.8 to 7.2 shifts it by 48 at the middle column, and moving triangle height from 3.2 to 4.8 shifts it by 48 at the middle row, so neither is the bigger lever here.
| Triangle base \ Triangle height | 3.2 | 4 | 4.8 |
|---|---|---|---|
| 4.8 | 76.8 | 96 | 115.2 |
| 5.4 | 86.4 | 108 | 129.6 |
| 6 | 96 | 120 | 144 |
| 6.6 | 105.6 | 132 | 158.4 |
| 7.2 | 115.2 | 144 | 172.8 |
The highlighted cell is the worked example: 120.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Triangle base | 6 | Enter the triangle base used in this calculation. |
| Triangle height | 4 | Enter the triangle height used in this calculation. |
| Prism length | 10 | Enter the prism length used in this calculation. |
| Volume | 120 | |
| Triangle base area | 12 | |
Inputs, definitions and assumptions
Triangle base
Enter the triangle base used in this calculation. The prefilled worked-example value is 6.
Triangle height
Enter the triangle height used in this calculation. The prefilled worked-example value is 4.
Prism length
Enter the prism length used in this calculation. The prefilled worked-example value is 10.
How to use this calculator
- 1Verify the inputs. Gather triangle base, triangle height and prism length from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the volume at 120. Store your own version of it as Scenario A.
- 3Test one change. Start with triangle base, the input with the biggest effect here: moving triangle base from 5.4 to 6.6 takes the volume from 108 to 132, a swing of 20% of the worked-example figure.
- 4Check the extremes. At half the example triangle base (3) the volume is 60; at double (12) it is 240.
People also ask
Frequently asked questions
How do you calculate triangular prism volume?
Base area = ½ × base × height; volume = base area × length. At the worked-example inputs the volume is 120.
What does the triangular prism volume result mean?
Find how much a wedge, a roof space or a tent holds. At the worked-example inputs the volume is 120. It rises with triangle base, triangle height and prism length.
How much does triangle base change the volume?
Holding every other input at the worked-example value, moving triangle base from 4.8 to 7.2 moves the volume from 96 to 144, a spread of 48.
What are the limits of this triangular prism volume calculator?
Formulas assume ideal geometric shapes. Real-world measurements carry their own error, and every input must use the same unit: mixing feet and inches silently produces a wrong answer. The tables on this page test triangle base only from 4.8 to 7.2; a value outside that range is not tabulated here.
Which input moves the volume most in the triangular prism volume calculator?
Ranked by how far each moves the volume across the range tested: triangle base (24, 20%), triangle height (24, 20%) and prism length (24, 20%).
If I double triangle base in the triangular prism volume calculator, does the volume double?
Doubling it from 6 to 12 takes the volume from 120 to 240, which is 2.00 times the worked-example figure. So the result scales almost exactly in proportion. Halving it to 3 gives 60.
How much does triangle height matter in the triangular prism volume calculator?
The worked example uses 4. With the other inputs left at the worked example, moving triangle height from 3.6 to 4.4 takes the volume from 108 to 132, a swing of 20% of the worked-example figure.
How much does prism length matter in the triangular prism volume calculator?
The worked example uses 10. Holding every other input at its worked-example value, moving prism length from 9 to 11 takes the volume from 108 to 132, a swing of 20% of the worked-example figure.
Which inputs change the triangle base area in the triangular prism volume calculator?
At the worked-example inputs it is 12. Triangle base takes it from 10.8 to 13.2 and triangle height takes it from 10.8 to 13.2.
Does it matter which units I use for area and volume calculators?
Yes, and consistently. If length is in feet, area comes out in square feet and volume in cubic feet automatically, but only if every input uses the same base unit. Mixing feet and inches in one calculation silently produces a wrong answer with no error shown.
Sources and evidence
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